Solve the initial value problem dy/dx = −(2x cos(x^2))y +
6(x^2)e^(− sin(x^2)) , y(0) = −5
Solve the initial value problem dy/dt = (6t^5/(1 + t^6))y + 7(1
+ t^6)^2 , y(1) = 8.
Find the general solution of dy/dt = (2/t)*y + 3t^2* cos3t
Prove the follwing statements
Suppose that S is a linearly independent set of vectors in the
vector space V and let w be a vector of V that is
not in S. Then the set obtained from S by adding w
to S is linearly independent in V.
If U is a subspace of a vector space V and dim(U)=dim(V), then
U=V.
f (x) = -0.248226*cos (2 x) - 0.0184829*cos ((2+2)x) -
0.0594608*cos(x)*sin(x) + 0.123626*sin ((2+2)x).
The intervall is ]0, 3/2[
What is the local maximum and local minimum? Answer with 5
decimals